Monday, June 15, 2015
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Two weeks ago, I discussed the sign conventions and the stupidity of the people who can't comprehend that another sign convention is just as good. A similar exchange arose in the Ráchel Doležal thread.

Apparently, many Americans are convinced that people can't possibly conveniently measure things in the everyday life using the metric system units. For a while, I thought that all of them were joking but this meme was so omnipresent that I decided that they actually believe this idea. There can't be life outside the Anglo-Saxon world! Or perhaps, all the Europeans are secretly measuring and thinking in inches and pounds and they only convert the numbers to centimeters and kilos whenever the evil governments are watching them and they want to save their lives.

Are you joking? This kind of conspiracy theory is just totally incredible. Almost no one in Europe can quickly estimate real-world quantities in the medieval units anymore. I can't really do it "automatically", either, even though I have lived in the U.S. for 10 years. From my viewpoint, the medieval system is counterintuitive, hard to reason or calculate with, and metric4us.com convincingly argues that it is more difficult for Americans, too!

People needed to measure distances and lengths, masses, and time for thousands of years. In this sense, some primitive portions of "physics" are very old. The "contemporary" medieval Anglo-Saxon units were inspired by the units in the Roman Empire which included lots of feet and inches of various types.

Up to some moment, inches and feet may be convenient because you need nothing else than your body – something you have gotten from Mother Nature – to measure. Clearly, every body is different. After some time, people realize that and acknowledge the inaccuracy that follows from this diversity. But they're used to measure things in "human organs" and they're used to the numerical values. So they invent prototypes and rulers and weights that play the same role as the human organs but do so more accurately. In the 20th century, more abstract "rulers" such as the wavelength of some radiation became widespread and the accuracy of the measurements was greatly improved.

Let me begin with the inch. If I understand well, and I am not quite 100% certain, it was supposed to be the width of a thumb (one of the five fingers that, for reasons I don't fully understand, native English speakers don't consider to be fingers). If I place the thumb on the table and make it as wide as possible, it has about 2.4 centimeters.

The word "inch" doesn't actually mean a "thumb" in any language. Instead, the word "inch" is derived form Latin "uncia" which means "1/12": yes, one inch was meant to be 1/12 of a foot, a relationship that was preserved up to the present form of the medieval units. You may notice that "uncia" ("1/12" in Latin) also sounds like an "ounce", a modern medieval unit of weight. Unfortunately, one ounce is no longer equal to 1/12 of any important unit. To make things really bad, one "modern" ounce is exactly 1/16 of a "modern" pound. Given the fact that "uncia" means "1/12", this rule sucks, doesn't it? If you care, one Troy ounce was equal to 1/12 of one Troy pound.

Let me return to the inch. The different individual people's thumbs are different and the error you get by using thumbs – as if all thumbs were the same – is therefore huge. In fact, even if you average the thumbs over many people, the accuracy will remain hugely unsatisfactory. So historically, one inch was equal to:

The deviations are significant. In particular, Spain and Portugal are neighbors but the difference between their inches was a whopping 18%.

In 1756, our formidable empress Maria Theresa published a regulation and standardized the inch to be 26.34 mm. But you know, such regulations don't always change the habits of the people. So folks in Prague happily continued to use the old Roman inch which is 24.69 mm (not shown in the table above).

One of the minor points I want to make is that an old unit that everybody "knows" but everybody interprets "somewhat differently" is actually a liability, not an asset. If the meaning of a word (a unit) becomes this ambiguous, it is better to switch to a completely new one. It's just another reason to do so.

In 1791, Marquis de Condorcet, a French political scientist and mathematician, stated: "The metric system is for all people for all time." He realized that those medieval units were getting ludicrous and it was possible to switch to better ones.

In the following decade, the First French Republic was deciding about the new units and the units we (Europeans) know and love were pretty much established. In particular, 1 meter was chosen so that the circumference of a meridian is 40,000 km exactly (it is no longer the case but that's how the units was originally motivated). And 1 gram was the mass of one cubic centimeter of water.

The French produced lots of rulers and books and platinum-iridium prototypes and other things to be sure that the transition was ready and in 1799, the First French Republic introduced those new units by a law.

For a while, those units were only winners in France. On July 23rd, 1871, our deputies approved a new law that switched the whole Western half of Austria-Hungary (i.e. Austria and the Czech lands etc.) to the metric units. All rulers and weights had to be denominated in those new units. I believe that both France and Austria got used to the metric system very quickly.

In 1875, a conference decided that those units would be adopted pretty much internationally. The Prussians who just humiliated the French wanted to become the "masters" of the new units but the French managed to defend the international "ownership" over the new units and headquarters in an international city rather than a German one, namely in Paris. ;-)

The oldest person in the Czech Republic is about 110 years old so I assure you that no one in my homeland remembers the time when inches and feet were more widespread than centimeters and decimeters. The transition is not always smooth. The United Kingdom officially switched to the metric system in 1966. In the real everyday life, they still seem to be stuck with the medieval units.

Again, almost no continental European intuitively knows how much an inch, foot, ounce, pound, Fahrenheit degree etc. etc. is. So they obviously can't have any intuition about their magnitude. About their height in inches or feet. About their weight in pounds. The volume of their car tank in gallons. About the temperature in the morning in the Fahrenheit degrees. And so on. We simply don't have a clue and can't have a clue. Those medieval units are extinct and they are in no way needed.

If you are an American and you want to know how the Europeans talk about some temperature or length or weight or anything, just find the conversion somewhere on the Internet, convert your quantity to the SI units, and that's exactly what the Europeans say. The body temperature is about 37 °C and most people would define a terrible fever as 40 °C or more. You want to know whether a pizza is baked in the oven at 200 °C or 250 °C. That's what almost everyone knows. No one has a clue how many Fahrenheit degrees it should be.

Another incredibly silly claim made by some of the champions of the medieval system is that the "nice numerical multiples" of ounces and pounds and gallons etc. are "more convenient in the supermarkets" or other shops. Oh, really?

I assure you that almost all cardboard packages of milk are 1 liter (cubic decimeter) here. Olive oil is either 3/4 or 1 liter. Bottled water or soda is either 1.5 or 2 liters. Sugar is most often sold in exact 1-kilogram bags. Almost all beer bottles, cans, and "big glasses of beer" (the most typical amount of beer that a Czech drinks with his lunch) in the pub are exactly 0.5 liters, much like many heavy alcoholic beverages. It is a tradition to sell wine in exact 0.7 liter bottles. Potato chip bags are usually 100 grams or 150 grams. You may buy a 10-meter roll of tape. And 30-meter or 50-meter oral thread. Bags of cement are 25 kilos or 50 kilos. The area of the A0 sheet of paper is exactly one squared meter; A4 therefore has 1/16 of a squared meter. Everyone knows how much he pays for 1 kilowatthour of electricity – and not for 1 dozen-dozen-foot-pound of it. The most standard "full" Edison light bulbs used to have exactly 100 watts – before smaller (and then energy-efficient) bulbs began to spread. In 1997, the maximum allowed car speed in Czech cities was lowered from 60 km/h to 50 km/h. On superhighways, the limit went from 110 km/h to 130 km/h. The normal atmospheric pressure happens to be very close to 100 kPa = 1000 hPa (hectopascals) – a helpful coincidence. The freezing point of water is 0 °C, the boiling point is 100 °C. The room temperature is 20-24 °C. When the daily temperature high is above 30 °C, we talk about a tropical day. "Nice numbers" are everywhere. If some number weren't nice, of course it's easy to adjust the package etc. and sell a slightly different one with a nice number. All these things at least as perfectly convenient as some "nice numbers" in pounds, ounces, gallons, or whatever. The idea that "nice multiples" of the imperial units are "more convenient" is another self-evident and pure superstition.

In science, we don't want to learn too many (verbal) prefixes etc. which is why only the prefixes that are (positive or negative) powers of 1,000 are common. They're enough – numbers between 0.5 and 500 sound natural enough. You won't overlook zeroes easily. But in the everyday life, prefixes linked to other powers of ten are used, too. For example, most Czech women buying meat will ask for 20 decagrams (deca = 10) instead of 200 grams of meat or ham (I have always asked for 200 grams because this deca- stuff looked archaic to me!). The most widespread "panák" (short drink) of whisky (or a similar beverage) has 5 cl i.e. 5 centiliters (centi = 1/100, just like for centimeters). Women may drink just "2 deci" (deciliters, deci = 1/10) of wine. On the other hand, breweries produce much more beer so their tradition is to measure the beer in hectoliters (hecto = 100). You may sell fields in hectars (100 ares, 10,000 squared meters). As you could see, between \(10^{-3}\) and \(10^{+3}\), all the prefixes are common: milli, centi, deci, one, deca, hecto, kilo. It's only the "more extreme multiples" that are almost always powers of 1,000. (The most important, mostly extinct exception is myria-. A myriad is technically the number 10,000. In 1795, it was still recommended to use myriameters i.e. 10 km. I can't resist to mention that our Indian friends have their own modified decimal numbering system. One hundred thousand is written as 1,00,000 and called lakh. Crore, 1,00,00,000 is similarly ten million. The SI system "prefers" the powers of one thousand but it's just another part of the conventions that could have been decided differently.)

There are some units outside the metric system which remained dominant even in Europe. So the energy stored in food (and sometimes heat) is often expressed in "calories". This word actually means "kilocalories" in the more technical sense. People know that a woman needs to eat about 1,500 kcal and a man needs 2,000 kcal a day. If I want to tell you the value in the SI units, joules, I have to multiply by 4.2 or so. I have internalized the values in kcal because that's what most people around talk about. Similarly, we use the non-decimal multiples of one second, of course, like a minute, an hour, a day, a week, and so on. I am sure that people could get used to decimal multiples of a base unit – and produce different watches and clocks – as well but this simply hasn't taken place. But a day could easily become the base unit of time. A deciday would be 2.4 hours (144 minutes); a long movie would take about a deciday. A centiday would be 864 seconds i.e. 14.4 minutes, a milliday would be 1.44 minutes. Prepare popcorn for 1-3 millidays. A microday would be about the "flash", about one-half of the reaction time of your brain, 0.0864 second. Stop the microwave oven when the popcorn pops less than once in 30 microdays in average. In Czech, we usually "measure" one second by saying "jednadvacet" (twenty-one). We would have other tools, like saying "ten microdays, ten microdays". Each time you say "ten microdays", you get older by ten microdays. Of course we could eliminate all the old units if we wanted. But the benefits would arguably be limited relatively to the transition costs. Watches and clocks etc. are still too expensive and people are used to too many schedules etc.

I guess that the attempts to switch the U.S. from the medieval units to the SI units (which is also the core of the program of Lincoln Chafee, an unknown Democrat Party presidential candidate) are hopeless because not only the Americans are heavily used to the medieval units. Tons of them aren't even capable of understanding that it is possible to switch! They don't understand that the medieval units aren't needed for anything at all and that life adapts to new units so that everything is basically equally practical or convenient (or more so, if the multiples are easier to calculate with).

One of the cutest "moderate attitudes" was expressed by a comment by an American who claimed that it's perhaps possible to use the SI units in engineering but it's surely impossible for humans to use the SI units in the everyday life. Holy cow, are you serious? Why should engineering have a greater "intrinsic proximity" to the SI units than the everyday life? You might very well have a country, an anti-America, which would be using the SI units in the everyday life and the medieval units in engineering (perhaps to please their American trade partner).

Why not? In fact, how do you distinguish engineering from the everyday life? A kilogram of iron is OK in kilograms but apples must be "naturally" measured in pounds? Why would you believe such complete nonsense? After all, a vegetable shop owner may find the mass of apples by placing them on a scale and the one-kilogram weight that is placed on the other side was produced by some engineers. You just can't separate the contexts to "engineering" and "everyday life" in any meaningful or useful way. They are pretty much the same thing. It's obvious that if people can get used to some units in one context, they may get used to them in the other context(s), too.

Many Americans' bigotry about their medieval units is just a very special example of a much more general troublesome phenomenon. These Americans – and, apparently to a lesser extent, many other people – just aren't able or willing to distinguish their arbitrary cultural baggage and habits – something that they were trained to do, say, and believe in a certain way, along with millions of other people – from objective truths and universal values. It's the same with religions etc. What was the name of the crazy hippie 2,000 years ago? Yup, Christ. Jesus Christ! It's just one guy among millions in the history who claimed to have some supernatural skills or contacts with the fundamental layers of the Universe. He differs from the millions of others by having gotten more popular for largely arbitrary and irrational reasons.

(Christ isn't a characteristically American example. There exist countries even here in Europe where this particular fad is still alive and kicking.)

You can try to sell Him as one of the most important things in Nature but it's analogously silly to suggesting that women can't trace their weight if they don't know pounds. Jesus Christ, like an inch, is arbitrary cultural baggage. And so is feminism, Eminem, and many other things. If you're at least remotely rational, you just can't possibly believe that all people on Earth – if not all intelligent beings in the Universe – will be obsessed by these things.

It seems to me that the larger nation you deal with, the less able it may be to figure out that other nations generally don't share its conventions.

In science, we prefer various \(1=c=\hbar=k_B=\epsilon_0\) units with the only dimensionful quantity based on \(1\GeV\), for example (in particle physics), unless we set \(G=1\) or \(\alpha'=1\) etc. And I actually think that the world would be a better place if the everyday life were switched to base-10 multiples of these "more fundamental" units, too. But in the real world, dreams about such rationalization of the units that people are actually using in their lives seem hopeless when so many people can't even comprehend that life is equally possible without pounds and inches!

One more comment. Of course, even our usage of the decimal system is just a convention we got used to. If children were analogously trained to use e.g. the hexadecimal (base-16) system, they would do it as well as we can deal with the decimal system! Almost no one really uses fingers and thumbs to count so this argument is not too important. If children were trained to the hexadecimal system, they would become closer friends of their computers, too. ;-) One would have no problem with the fact that the year right now is 7DF, Anno Domini sevendred-deezehnpty-efzehn. In 21 (=33) i.e. twenpty-one years, we would have the year eightdred (800=2048) – a new cenbytery would start (2.56 centuries). Needless to say, in such a system, the international system of units would surely prefer prefixes based on the powers of 16 or \(16^3 = 2^{12} = 4,096\) to make things convenient. Everything would be adapted to that system and would be at least as practical and convenient as our base-10 world. Please, if you have any doubts about it, you have to think about it more carefully because you are missing something absolutely essential about the relationship between the real world and terminology/conventions.